Framework #14 — Sweep line vs sorting vs greedy for intervals

INTERVALS — APPROACH SELECTION
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SORT + MERGE:
  Sort by start, merge overlapping
  □ Merge intervals
  □ Insert interval (merge after insert)
  □ Interval intersection
  Time: O(n log n)

SORT + GREEDY:
  Sort by end time, pick earliest-ending first
  □ Activity selection / max non-overlapping
  □ Meeting rooms: can one person attend all?
  □ Minimum meeting rooms (sort starts + ends)
  Time: O(n log n)

SWEEP LINE:
  Create events: +1 at start, -1 at end
  Sort events, scan left to right
  □ Maximum overlap count
  □ Skyline problem
  □ Rectangle area union
  Time: O(n log n)

DECISION:
  Merge overlapping?           → sort by start, merge
  Max non-overlapping?         → sort by end, greedy
  Count overlaps at a point?   → sweep line
  "How many rooms needed?"     → sweep line or sort both arrays
  Need new merged list?        → sort + merge
  Need selection subset?       → sort + greedy